In the construction industry, a “project labor agreement” (PLA) between clients and contractors stipulates that all bidders on a project will use union labor and abide by union rules. The article “Do Project Labor Agreements Raise Construction Costs?” (CS-BIGS 2007: 71–79) investigated construction costs for 126 schools in Massachusetts over an eight-year period. Among the variables considered were y = project cost, in dollars per square foot; x₁ = project size, in 1000s of ft²; x₂ = 1 for new construction and 0 for remodel; and x₃ = 1 if a PLA was in effect and 0 otherwise.

a. What would it mean in this context to say that x₁ and x₃ have an interaction effect?
b. What would it mean in this context to say that x₂ and x₃ have an interaction effect?

c. No second-order terms are statistically significant here, and the estimated regression equation for the first-order model is y = 138.69 – .1236 x₁ + 17.89x₂ + 18.83x₃. Interpret the coefficient on x₁. Does the sign make sense?
d. Interpret the coefficient on x₃.

e. 

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The estimated standard error of 3 is 4.96. Test the hypotheses Ho: P3 = 0 Vs. Ha: B3> 0 at the .01 significance level. Does the data indicate that PLAS tend to raise construction costs?